Soru Lineer cebir

Zamanı geçmiştir herhalde ama yine de ancak fırsatım olduğu için bugün tekrar bakabildim. Hiç yoktan iyidir.

A matrisi için sadece skaler olmama şartı verildiğinden şöyle seçilebilir:

https://i72.servimg.com/u/f72/19/97/10/39/a_matr10.png

a) det(A) = A matrisinde a(3, 3) elemanının değeri.
b) Köşegenlenebilir, görüldüğü gibi A matrisi zaten kolaylık olması amacıyla bu şekilde seçildi.
c) Köşegen elemanları keyfi şekilde değiştirilip birçok A matrisi bulunabilir.

WolframAlpha Hesapları:
https://www.wolframalpha.com/input/?i=matrix addition &assumption={"F", "MatricesOperations", "theMatrix2"} ->"2{{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1}}"&assumption={"F", "MatricesOperations", "theMatrix1"} ->"{{1,0,0,0,0},{0,-1,0,0,0},{0,0,-2,0,0},{0,0,0,1,0},{0,0,0,0,-1}}"&assumption={"C", "matrix addition"} -> {"Calculator"}

https://www.wolframalpha.com/input/?i=matrix power({{1,0,0,0,0},{0,-1,0,0,0},{0,0,-2,0,0},{0,0,0,1,0},{0,0,0,0,-1}}, 2)

https://www.wolframalpha.com/input/?i=matrix power({{1,0,0,0,0},{0,-1,0,0,0},{0,0,-2,0,0},{0,0,0,1,0},{0,0,0,0,-1}}, 3)

https://www.wolframalpha.com/input/?i=matrix addition &assumption={"F", "MatricesOperations", "theMatrix3"} ->"{{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1}}"&assumption={"F", "MatricesOperations", "theMatrix2"} ->"{{1,0,0,0,0},{0,-1,0,0,0},{0,0,-8,0,0},{0,0,0,1,0},{0,0,0,0,-1}}"&assumption={"F", "MatricesOperations", "theMatrix1"} ->"{{1,0,0,0,0},{0,-1,0,0,0},{0,0,-2,0,0},{0,0,0,1,0},{0,0,0,0,-1}}"&assumption={"C", "matrix addition"} -> {"Calculator"}

https://www.wolframalpha.com/input/?i=matrix power({{3,0,0,0,0},{0,-1,0,0,0},{0,0,-9,0,0},{0,0,0,3,0},{0,0,0,0,-1}}, 2)

https://www.wolframalpha.com/input/?i=matrix addition &assumption={"F", "MatricesOperations", "theMatrix3"} ->"{{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1}}"&assumption={"F", "MatricesOperations", "theMatrix2"} ->"{{1,0,0,0,0},{0,-1,0,0,0},{0,0,-8,0,0},{0,0,0,1,0},{0,0,0,0,-1}}"&assumption={"F", "MatricesOperations", "theMatrix1"} ->"{{1,0,0,0,0},{0,-1,0,0,0},{0,0,-2,0,0},{0,0,0,1,0},{0,0,0,0,-1}}"&assumption={"C", "matrix addition"} -> {"Calculator"}

https://www.wolframalpha.com/input/?i=matrix power({{3,0,0,0,0},{0,-1,0,0,0},{0,0,-9,0,0},{0,0,0,3,0},{0,0,0,0,-1}}, 3)

https://www.wolframalpha.com/input/?i=matrix multiplication&assumption={"F", "MatricesOperations", "theMatrix3"} ->"{{27,0,0,0,0},{0,-1,0,0,0},{0,0,-729,0,0},{0,0,0,27,0},{0,0,0,0,-1}}"&assumption={"F", "MatricesOperations", "theMatrix2"} ->"{{9,0,0,0,0},{0,1,0,0,0},{0,0,81,0,0},{0,0,0,9,0},{0,0,0,0,1}}"&assumption={"F", "MatricesOperations", "theMatrix1"} ->"{{3,0,0,0,0},{0,1,0,0,0},{0,0,0,0,0},{0,0,0,3,0},{0,0,0,0,1}}"&assumption={"C", "matrix multiplication"} -> {"Calculator"}

https://www.wolframalpha.com/input/?i=determinant of {{1,0,0,0,0},{0,-1,0,0,0},{0,0,-2,0,0},{0,0,0,1,0},{0,0,0,0,-1}}
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Rica ederim, keşke tam yardımcı olabilecek kadar teorik lineer cebir bilgim olsaydı.